Multiplicative integration RNN (MIRNN) [1]} is yet another approximation of higher order/tensor RNNs [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. This model uses a Hadamard product \(\odot \)  instead of a sum operation \(+\)  in the standard RNN update rule. Hence, this new formulation allows for a potentially more powerful for the RNN to update its hidden state without introducing any extra parameters. This change can be written in the following manner:
\(\mathbf {z}_t = f1(U \mathbf {x}_t \odot R \mathbf {z}_{t-1}) \mbox{.}\) 
